Ischyrhiza was named by Leidy (1856) [Sepkoski's age data: K Ceno-u K Maes Sepkoski's reference number: 884]. It is not extant.

It was reranked as Onchosaurus (Ischyrhiza) by Arambourg (1940); it was corrected as Ischirhiza by Cappetta (1973).

It was assigned to Squalidae by Leidy (1860); to Luciidae by Hay (1902); to Onchosaurus by Arambourg (1940); to Esocidae by Rapp (1946); to Ganopristinae by Estes (1964), Cappetta (1973) and Storer and Johnson (1974); to Pristidae by Miller (1967), Estes and Berberian (1970), Thurmond and Jones (1981) and Bryant (1989); to Galeomorphii by Sepkoski (2002); and to Sclerorhynchidae by Cappetta and Case (1975), Herman (1977), Case (1978), Case (1979), Uyeno and Hasegawa (1986), Cappetta (1987), Case and Schwimmer (1988), Case (1991), Nessov (1997), Cappetta and Case (1999), Peng et al. (2001), Pearson et al. (2002), Cicimurri (2003), Suárez and Cappetta (2004), Bourdon et al. (2011), Otero et al. (2013), Cicimurri et al. (2014), Bice and Shimada (2016), Hoganson et al. (2019) and Maisch et al. (2021).